Evaluate the following integrals. \int \frac{e^{x}}{4e^{x}+6}dx

Teddy Dillard 2021-12-11 Answered
Evaluate the following integrals.
ex4ex+6dx
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

veiga34
Answered 2021-12-12 Author has 32 answers

Step 1
To evaluate: ex4ex+6dx
Solution:
Let substitute t=4ex+6
Differentiating both sides,
dtdx=ddx(4ex+6)
dtdx=4ex+0
dtdx=4ex
dt4ex=dx
Step 2
Substituting the values in given integral,
ex4ex+6dx=extdt4ex
=141tdt
=14ln|t|+C
Put back t=4ex+6
ex4ex+6dx=14ln|4ex+6|+C
Hence, required answer is 14ln|4ex+6|+C.

Not exactly what you’re looking for?
Ask My Question
Mary Herrera
Answered 2021-12-13 Author has 37 answers

ex4ex+6dx
We put the expression exp(x) under the differential sign, i.e.:
exdx=d(ex),t=ex
Then the original integral can be written as follows:
14t+6dt
14x+6dx
Calculate the table integral:
1212x+3dx=ln(2x+3)4
Answer:
ln((2x+3)14)+C
To write down the final answer, it remains to substitute exp(x) instead of t.
ln(2ex+3)4+C

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more